Game Development Reference
In-Depth Information
Figure 8-1.
Force balance on a car driving in a straight line on a horizontal surface
As you can see from Figure 8-1, there are quite a few forces acting on the car, so let's go
over them one by one. The force of gravity pulls the car towards the earth. It acts both normal
to the slope with a force,
F
gN
=
mg
cos
q
, as well as parallel to the slope with a force,
F
gP
=
mg
sin
q
.
Depending on whether the car is pointing uphill or downhill, the parallel component of gravi-
tational force can pull the car either forwards or backwards.
This force of gravity in the normal direction,
F
gN
, is balanced by normal forces,
F
Nf
and
F
Nr
,
that act along the surfaces of the front and rear tires that are in contact with the ground. The
total normal force,
F
N
, is the sum of the forces on the front and rear tires and is equal to the
mass of the car multiplied by the acceleration due to gravity and the cosine of the slope angle,
q
.
FF F
=+=
gq
cos
(8.1)
N
Nf
Nr
The engine generates torque, which when applied to the wheels causes them to rotate.
Friction between the tires and the ground resists this motion, resulting in a force applied to the
tires in the direction opposite to the rotation of the tires. The force applied to the tires,
F
T
, is
equal to the torque applied to the wheels,
T
w
, divided by the wheel radius,
r
w
.
T
F
=
w
w
(8.2)
r
T
As we shall see in the “Gears and Wheel Torque” section a little later in this chapter, the
torque applied to the wheels is generally not equal to the torque generated by the engine.
When the car is in motion, an aerodynamic drag force will develop that will resist the
motion of the car. As we saw in Chapter 5, drag force can be modeled as a function of the air
density,
r
, frontal area,
A
, the square of the velocity magnitude,
v
, and a drag coefficient,
C
D
.
1
2
2
FCv A
=
r
(8.3)
D
D
